Nonlinear equality constraints in feasible sequential quadratic programming

被引:52
作者
Lawrence, CT
Tits, AL
机构
[1] UNIV MARYLAND,SYST RES INST,COLLEGE PK,MD 20742
[2] UNIV MARYLAND,DEPT ELECT ENGN,COLLEGE PK,MD 20742
关键词
constrained optimization; nonlinear equality constraints; sequential quadratic programming; feasibility;
D O I
10.1080/10556789608805638
中图分类号
TP31 [计算机软件];
学科分类号
081202 ; 0835 ;
摘要
A simple scheme is proposed for handling nonlinear equality constraints in the context of a previously introduced sequential quadratic programming (SQP) algorithm for inequality constrained problems, generating iterates satisfying the constraints. The key is an idea due to Mayne and Polak (Math. Progr., vol. 11, pp. 67-80, 1976) by which nonlinear equality constraints are treated as ''less than or equal to''-type constraints to be satisfied by all iterates, thus precluding any positive value, and an exact penalty term is added to the objective function, thus penalizing negative values. Mayne and Polak obtained a suitable value of the penalty parameter by iterative adjustments based on a test involving estimates of the KKT multipliers. We argue that the SQP framework allows for a more effective estimation of these multipliers, and we provide convergence analysis of the resulting algorithm. Numerical results, obtained with the CFSQP code, are reported.
引用
收藏
页码:265 / 282
页数:18
相关论文
共 12 条
[1]   AVOIDING THE MARATOS EFFECT BY MEANS OF A NONMONOTONE LINE SEARCH .2. INEQUALITY CONSTRAINED PROBLEMS - FEASIBLE ITERATES [J].
BONNANS, JF ;
PANIER, ER ;
TITS, AL ;
ZHOU, JL .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1992, 29 (04) :1187-1202
[2]  
Daniel J. W., 1973, Mathematical Programming, V5, P41, DOI 10.1007/BF01580110
[3]  
*HARW SUBR LIBR, 1985, LIBR REF MAN
[4]   A 2-STAGE FEASIBLE DIRECTIONS ALGORITHM FOR NONLINEAR CONSTRAINED OPTIMIZATION [J].
HERSKOVITS, J .
MATHEMATICAL PROGRAMMING, 1986, 36 (01) :19-38
[5]  
HOCK W, 1981, LECTURE NOTES EC MAT, V187
[6]  
LAWRENCE C, 1995, USERS GUIDE CFSQP VE
[7]  
MARATOS N, 1978, THESIS IMPERIAL COLL
[8]   FEASIBLE DIRECTIONS ALGORITHMS FOR OPTIMIZATION PROBLEMS WITH EQUALITY AND INEQUALITY CONSTRAINTS [J].
MAYNE, DQ ;
POLAK, E .
MATHEMATICAL PROGRAMMING, 1976, 11 (01) :67-80
[9]   ON COMBINING FEASIBILITY, DESCENT AND SUPERLINEAR CONVERGENCE IN INEQUALITY CONSTRAINED OPTIMIZATION [J].
PANIER, ER ;
TITS, AL .
MATHEMATICAL PROGRAMMING, 1993, 59 (02) :261-276
[10]  
SCHITTKOWSKI K, 1987, LECTURE NOTES EC MAT, V282